Pour 1/2 tablespoon of oil into a large frying pan then add eggs. Scramble into medium-sized pieces then transfer to plate. Set aside.
In a saucepan, mix together peanut oil, peanut butter, water, soy sauce, milk, brown sugar and lemon juice. Season with garlic powder and paprika. Heat until sauce is smooth. Season liberally with cayenne.
Drain noodles; noodles should be very flexible, but still relatively firm. Heat remaining 1 1/2 tablespoons vegetable oil in a large saucepan or wok. Cook noodles in oil, stirring constantly, until they are tender, about 2 minutes. Stir in peanut sauce, sprouts, carrots, green onions, ground peanuts and the scrambled eggs. Continue to cook over low heat until vegetables are crisp-tender, about 5 minutes. Serve immediately, garnished with lime wedges.